The smooth endoplasmic reticulum (SER) is a network of membrane-enclosed sacs and tubules found in eukaryotic cells. It plays a crucial role in various cellular functions. However, one of the functions mentioned in the options is not carried out by the smooth endoplasmic reticulum. Let's explore each option in detail:

a) Transport of materials:
The smooth endoplasmic reticulum is involved in the transport of materials within the cell. It helps in the movement of lipids, proteins, and other molecules between different cell compartments. It acts as a highway for the transport of these materials.

b) Synthesis of lipid:
One of the primary functions of the smooth endoplasmic reticulum is the synthesis of lipids. It contains enzymes involved in lipid metabolism, including the synthesis of phospholipids, cholesterol, and steroid hormones. Lipids synthesized in the smooth endoplasmic reticulum are used in various cellular processes and are also important for the structure and function of cell membranes.

c) Synthesis of protein:
Contrary to the other options, the synthesis of proteins is not primarily carried out by the smooth endoplasmic reticulum. Protein synthesis occurs mainly in the ribosomes, which can be free in the cytoplasm or attached to the rough endoplasmic reticulum. The rough endoplasmic reticulum is studded with ribosomes and is responsible for the synthesis of proteins that are destined for secretion or insertion into the cell membrane.

d) Synthesis of steroid hormone:
The smooth endoplasmic reticulum is involved in the synthesis of steroid hormones. It contains enzymes that catalyze the production of various steroid hormones, such as cortisol, estrogen, and testosterone. These hormones play essential roles in the regulation of various physiological processes.

In summary, the function not carried out by the smooth endoplasmic reticulum is the synthesis of proteins. Protein synthesis primarily occurs in the ribosomes, which can be free in the cytoplasm or attached to the rough endoplasmic reticulum. The smooth endoplasmic reticulum is primarily involved in the transport of materials and the synthesis of lipids and steroid hormones.